Bagram district chief Darwaish Raufi said Sunday that the surrender handed the one-time American base over to the insurgents.
The men were offered food and temporary accommodation in Uzbekistan, and the ministry was in touch with Afghan officials regarding the return of Afghan soldiers to their home country.
US troops will also help in the evacuation of Afghans who worked with the military during the nearly two-decade war.
Afghan president delivers televised address, first public remarks in days following major Taliban advance
The lightning advance comes less than three weeks before the US is set to withdraw its last forces after nearly 20 years of war.
The Taliban have seized control of much of rural Afghanistan since foreign forces began the last stage of their withdrawal in early May, but are now focused on capturing provincial capitals.
Gen Ahmadzai was scheduled to hold wide-ranging talks with top Indian military brass including his counterpart Gen MM Naravane and National Security Advisor Ajit Doval.
The incident occurred late on Sunday night in Arundu sector in the country's Chitral district when an Afghan National Army local Commander requested the Pakistan Army for refuge.